Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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[Item 1.]
[2.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. & ARCHIMEDIS ASVMPTOR VM LIBER.
[3.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. PARAPHRASTE ABALPHATO ASPHAHANENSI
[4.] ADDITVS IN CALCE ARCHIMEDIS ASSVMPTORVM LIBER, EX CODICIBVS ARABICIS M.SS. SERENISSIMI MAGNI DVCIS ETRVRIÆ ABRAHAMVS ECCHELLENSIS MARONITA
[5.] IO: ALFONSVS BORELLVS
[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.
[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.
[8.] CAVE CHRISTIANE LECTOR.
[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.
[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.
[11.] PRÆFATIO AD LECTOREM.
[12.] INDEX
[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.
[14.] II.
[15.] III.
[16.] IV.
[17.] V.
[18.] VI.
[19.] VII.
[20.] VIII.
[21.] IX.
[22.] X.
[23.] XI.
[24.] XII.
[25.] XIII.
[26.] XIV.
[27.] XV.
[28.] XIV.
[29.] NOTÆ.
[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.
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page |< < (73) of 458 > >|
11173Conicor. Lib. V.
Notæ in Propoſit. XXIX. XXX.
& XXXI.
A Lioquin producatur perpendicularis C E, & c. Exiſtente C A lineæ
11a breuiſsima, &
A D tangente, ſi C A non eſt perpendicularis ad tangen-
tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
eam in E, &
ſectionem in F, erit in triangulo A C E angulus C A E acutus,
&
minor angulo recto E, & propterea C A ſubtendens maiorem angulum re-
ctum, maior erit quàm C E, quæ acutum ſubtendit:
cumque punctum E tan-
gentis cadat extra ſectionem, erit C F minor, quàm C E;
ideoque C A multo
maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
hypotheſin.
Si vero fuerit D A C rectus, & c. Quia C A ſupponitur breuiſsima,
22b3333. 34.
lib. 2.
&
angulus D A C rectus, erit A D tangens; nam ſi hoc verum non eſt,
ducatur ex puncto A recta linea A G, contingens ſectionem in
A;
ſecabit vtique tangens A G ipſam D A, & erit an-
gulus C A G rectus nimirum contentus à breuiſsima
C A, &
tangente A G, ex proxime demon-
ſtrata propoſitione;
ergo duo anguli recti
C A D, &
C A G æquales ſunt
inter ſe, pars, &
totum, quod
eſt abſurdum.
93[Figure 93]

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